Question: Simplify the following expression: $ q = \dfrac{8}{-5x - 8} - \dfrac{-7}{9} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{8}{-5x - 8} \times \dfrac{9}{9} = \dfrac{72}{-45x - 72} $ Multiply the second expression by $\dfrac{-5x - 8}{-5x - 8}$ $ \dfrac{-7}{9} \times \dfrac{-5x - 8}{-5x - 8} = \dfrac{35x + 56}{-45x - 72} $ Therefore $ q = \dfrac{72}{-45x - 72} - \dfrac{35x + 56}{-45x - 72} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{72 - (35x + 56) }{-45x - 72} $ Distribute the negative sign: $q = \dfrac{72 - 35x - 56}{-45x - 72}$ $q = \dfrac{-35x + 16}{-45x - 72}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{35x - 16}{45x + 72}$